Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective

Xuezhen Tu; Kun Zhu; Nguyen Cong Luong; Dusit Niyato; Yang Zhang; Juan Li

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Incentive Mechanisms for Federated Learning: From Economic and Game Theoretic Perspective

Xuezhen Tu, Kun Zhu, Nguyen Cong Luong, Dusit Niyato, Yang Zhang, Juan Li

arXiv:2111.11850v1Nov 20, 2021cs.GTcs.LG

TL;DR

FL participation can be hindered by resource costs, privacy risks, unreliable behavior, and information asymmetry. This paper surveys economic and game-theoretic approaches for designing incentive mechanisms in FL. The reviewed approaches include reported results of 100% bad-client detection and at least 15.8% and 2.3% test-accuracy improvements in specified attack scenarios.

Problem
Resource consumption, privacy-leakage risk, unreliable behavior, and information asymmetry create challenges for motivating and regulating participation in FL.
Method
The paper comprehensively surveys FL fundamentals, economic and game-theoretic models, and their applications to incentive mechanism design.
Results
The reviewed approaches are reported to be effective; one algorithm detected 100% of bad clients and improved test accuracy by at least 15.8% and 2.3% in flipping and noisy scenarios, respectively.
Takeaways & Limitations
Economic and game-theoretic approaches provide mechanisms for motivating FL participation and designing interactions among model owners and data owners.

Abstract

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Federated learning (FL) becomes popular and has shown great potentials in training large-scale machine learning (ML) models without exposing the owners' raw data. In FL, the data owners can train ML models based on their local data and only send the model updates rather than raw data to the model owner for aggregation. To improve learning performance in terms of model accuracy and training completion time, it is essential to recruit sufficient participants. Meanwhile, the data owners are rational and may be unwilling to participate in the collaborative learning process due to the resource consumption. To address the issues, there have been various works recently proposed to motivate the data owners to contribute their resources. In this paper, we provide a comprehensive review for the economic and game theoretic approaches proposed in the literature to design various schemes for stimulating data owners to participate in FL training process. In particular, we first present the fundamentals and background of FL, economic theories commonly used in incentive mechanism design. Then, we review applications of game theory and economic approaches applied for incentive mechanisms design of FL. Finally, we highlight some open issues and future research directions concerning incentive mechanism design of FL.

I. INTRODUCTION

Federated learning trains a global model from clients’ local data without directly sharing raw data, but participation consumes resources and creates reliability and privacy challenges. This survey frames incentive mechanisms as a way to recruit and retain participants while addressing these challenges.

Federated learning fundamentals: FL lets data owners train local models and send model updates for aggregation into a global model without exposing raw data.The process repeats until the global model reaches an accuracy target.
Challenges motivating incentives: Clients consume computing and communication resources during local training, which can make self-interested clients unwilling to participate without sufficient compensation.Unreliable clients may also submit malicious updates, including poisoning attacks, that can undermine collaborative learning.
Incentive mechanism design: Incentive mechanisms must motivate participation, preserve client privacy, evaluate contributions, and limit costs across heterogeneous FL tasks.The survey identifies participant recruitment and retention, privacy guarantees, contribution evaluation, and sustainable operation under minimized incentive cost as central challenges.
Survey scope: The survey reviews FL fundamentals, economic and game-theoretic foundations, and applications of these approaches to incentive mechanism design.It also discusses open issues and future research directions.
FL architecture: A typical client-server FL architecture includes clients, communication infrastructure, an FL service platform, and service users or requesters.Clients contribute data and computational resources, while the platform aggregates local updates and broadcasts the global model.

B. Incentive Mechanism Design for Federated Learning: Concepts, Definitions, and Motivations

FL incentive mechanisms address resource costs, information asymmetry, and heterogeneous participant behavior by defining desirable properties for truthful, rational, efficient, fair, and budget-aware participation. They formalize participation, contribution measurement, and reward assignment as an incentive design problem.

Motivation: A desirable FL incentive mechanism should encourage participation despite resource consumption, privacy-leakage risk, and information asymmetry between the server and participants.These conditions motivate incentive design in practical FL implementations.
Design properties: Incentive compatibility requires participants to obtain optimal compensation by truthfully reporting their contributed resources and cost types.False reporting should not improve a participant’s revenue.
Design properties: Individual rationality requires each participant’s utility to be non-negative when joining FL.This property captures participation being acceptable to the participant.
Design properties: Budget balance requires total participant payments to remain no greater than the given budget, while computation efficiency requires polynomial-time selection and reward allocation.These properties constrain mechanism cost and computational complexity.
Formalization: An FL incentive mechanism is represented as I = (P, C, R), where participants provide resources, C measures contribution, and R assigns rewards based on that measurement.Fairness is also identified as important for sustainable participation and reward assignment.

1) Definition of Incentive Mechanism in FL:

FL incentive mechanisms determine participation and rewards through contribution evaluation, but evaluation must balance accurate measurement with transparency and practical information constraints. The survey categorizes evaluation methods by reported resources, marginal contribution, influence, and reputation.

Definition: Incentive design seeks an optimal participation level Q and reward R, typically through optimization such as utility maximization.The mechanism contains contribution evaluation and reward allocation phases.
Transparency and trust: Trusting a central server to measure contributions can reduce transparency, motivating blockchain-based peer-to-peer payment and scoring-rule approaches.These approaches replace or supplement centralized evaluation and encourage trustworthy model updates.
Contribution evaluation: Self-report methods evaluate contributions using participant-reported resources such as computational capacity or data size.This is described as the most straightforward evaluation approach.
Contribution evaluation: Shapley-value methods evaluate a data owner’s average marginal contribution across possible participation orders and federation subsets.The value v(S) denotes the utility of the model trained collaboratively by subset S.
Contribution evaluation: Influence-based methods measure how a client’s contribution affects the FL model’s loss function, while reputation mechanisms provide another basis for evaluation.Fed-Influence is described as quantifying individual-client influence for convex and non-convex loss functions.

3) Reward Allocation:

Reward allocation returns value to participants through advance offers or post-task payoff sharing, while game-theoretic models represent strategic interactions among model owners and data owners. These approaches seek stable strategies under participant competition, private information, and budget constraints.

Reward allocation: Offered-reward schemes determine payment before training according to contributed-resource quality or participant voting.They allocate compensation before the FL task is completed.
Reward allocation: Payoff-sharing schemes allocate rewards after task completion, with dynamic budget division addressing possible payment delays and fairness objectives.The stated objectives include contribution fairness, regret distribution fairness, and expectation fairness.
Game-theoretic approaches: Game theory models interactions in which model owners and data owners choose strategies that affect one another’s payoffs.Players are rational decision makers, and equilibrium represents a stable outcome where no player wants to change strategy.
Non-cooperative games: In non-cooperative games, selfish players maximize individual payoffs without cooperation, and competitive sellers can choose pricing strategies for computational resources.Such games are modeled with strategy sets and payoff functions for each player.
Non-cooperative games: Nash equilibrium gives a stable strategy profile in which no player can improve its payoff unilaterally, but games may have no equilibrium or multiple equilibria.The survey therefore emphasizes checking equilibrium existence and uniqueness.
Incomplete information: Bayesian games address incomplete information when a model owner knows only the occurrence probabilities of other players’ types, such as device reliability or reputation.The corresponding Bayesian Nash equilibrium uses beliefs about other players’ types and strategies.

2) Stackelberg Game:

Stackelberg games model sequential leader–follower decisions in which leaders move first and followers respond, supporting incentive design in FL. Backward induction derives the Stackelberg equilibrium and can give the leader a first-mover advantage.

2) Stackelberg Game:: Stackelberg games are sequential-move games in which leaders act first and followers respond after observing their strategies.They are also called leader–follower games and aim to model multi-agent decisions while maximizing both sides’ utility.
2) Stackelberg Game:: In the two-player formulation, one mobile device selects a pricing strategy as leader, while the other selects its strategy as follower.Each player seeks to maximize its own utility based on both players’ strategies.
2) Stackelberg Game:: The strategy pair (p∗_1, p∗_2) is a Stackelberg equilibrium when neither leader nor follower can improve utility through a unilateral strategy change.The equilibrium conditions compare each player’s utility at the solution with utility under an alternative nonnegative strategy.
2) Stackelberg Game:: Backward induction solves the follower’s optimization first and then substitutes that response into the leader’s optimization problem.This procedure exploits the leader’s knowledge of the follower’s response and produces the equilibrium strategies.
2) Stackelberg Game:: At the Stackelberg equilibrium, the leader’s utility is at least as high as in the corresponding Nash equilibrium, creating a first-mover advantage.In FL, this structure lets mobile devices set resource prices after observing the model owner’s resource needs or offered reward.

3) Coalitional Game:

The supplied passages define auction mechanisms and their terminology, but do not provide substantive material on coalitional games. They describe how auctions allocate FL commodities and determine prices through bidding.

3) Coalitional Game:: An auction allocates commodities such as training data, computational resources, or bandwidth and establishes prices through bidding.Its rules determine resource allocation and prices among market participants.
3) Coalitional Game:: In FL auctions, model owners or service requesters can act as bidders, while data owners or clients typically act as sellers.An auctioneer conducts price and winner determination, and may sometimes be the seller.
3) Coalitional Game:: Auction commodities in FL can be training-data units or computing-resource units offered by data owners.Participants may assign different private or public monetary valuations to these commodities.
3) Coalitional Game:: Buyer utility is the commodity valuation minus final payment, while seller utility is the payment received from buyers.For a model owner, utility can increase with global-model accuracy and decrease with total payments.
3) Coalitional Game:: Sealed-bid auctions hide bids from other bidders; first-price auctions charge the winner its highest bid, whereas Vickrey auctions charge the second-highest bid.The Vickrey payment rule is described as encouraging truthful bidding and has been used to address unreliable-client behavior in FL.
3) Coalitional Game:: VCG auctions generalize Vickrey auctions to multiple commodities, using payments based on the social-value loss caused by winning.This payment rule is described as strategy-proof or truthful and applicable to motivating IoT devices to report true values.

2) Forward, Reverse and Double Auction:

Forward, reverse, and double auctions organize competition from different market sides in FL. Combinatorial auctions allocate bundles of commodities but face generally NP-hard winner determination.

2) Forward, Reverse and Double Auction:: Forward auctions have multiple buyers submit bids to compete for items offered by one seller.They are classified from the seller’s side of the market.
2) Forward, Reverse and Double Auction:: Reverse auctions have multiple sellers submit asking prices to compete to sell items to one buyer.They are often combined with mechanisms such as sealed-bid reverse auctions.
2) Forward, Reverse and Double Auction:: Double auctions match multiple model owners and data owners by having buyers and sellers simultaneously submit bids and asks.The auctioneer sets a transaction price p that exceeds sellers’ asks and remains below buyers’ bids.
2) Forward, Reverse and Double Auction:: Combinatorial auctions let buyers bid on bundles of multiple commodities rather than individual commodities.The auctioneer determines allocation and winners using bids and seller capacity; in FL, this includes allocating network bandwidth to multiple service providers.
2) Forward, Reverse and Double Auction:: Winner determination in combinatorial auctions is generally NP-hard, so approximate methods such as Lagrangian relaxation can be used.The passage identifies the absence of a polynomial-time algorithm for finding the optimal allocation in general.
2) Forward, Reverse and Double Auction:: Contract theory addresses information asymmetry between selfish FL-market agents, while matching theory optimally pairs two disjoint agent sets according to utilities.Both are presented as tools for modeling dynamic, mutually beneficial relations among rational and competitive participants.

2) Matching Theory:

The supplied passages mainly review Stackelberg-game applications rather than matching theory. They show how leader–follower incentives coordinate rewards, participation, resource contributions, pricing, and energy-related services in FL markets.

2) Matching Theory:: The review characterizes Stackelberg games as useful for interactions among model owners, data owners, service providers, and users with conflicting objectives.Common objectives include revenue, utility, cost, and system performance.
2) Matching Theory:: In FL, a model owner can offer a reward first and data owners can then choose participation levels, forming a leader–follower incentive interaction.The cited framework adopts Stackelberg games to stimulate both sides’ participation.
2) Matching Theory:: In the initial Stackelberg application, a base station sets a reward and user equipments choose CPU resources to maximize utility.Higher rewards increase local-model generation and global accuracy but also increase the base station’s incentive cost.
2) Matching Theory:: A related game approach achieves up to 22% gain in offered reward over a heuristic approach at the same target accuracy, but assumes a single MEC-server leader.The approach uses KKT and first-order conditions to obtain user best responses before the server optimizes its reward.
2) Matching Theory:: Another hierarchical game reverses the roles: MEC operators act as seller-leaders, while a cloud coordinator acts as buyer-follower allocating sensing data under latency constraints.Theoretical analysis establishes existence of a unique Stackelberg equilibrium, while simulations show operators can raise prices to improve utility.
2) Matching Theory:: A two-layer Stackelberg game models service-provider pricing and user demand in one layer, then service-provider and data-owner interactions in another.User competition is modeled as a non-cooperative game, and users’ utility includes network effects, service quality, and payments.
2) Matching Theory:: Dynamic incentives produce higher social welfare than static incentives by selecting clients that adapt to a time-varying environment.The cited UAV-led framework has the UAV offer rewards and clients choose participation levels.
2) Matching Theory:: Stackelberg mechanisms also coordinate energy and training decisions across wireless-power nodes, edge devices, MEC nodes, and service requesters.The WPEG framework jointly optimizes power transmission and economic rewards to maximize the utility of wireless-power nodes and edge devices.

B. Incentive Mechanisms Based on Non-cooperative Game

Non-cooperative game mechanisms model strategic interactions among FL buyers, sellers, clients, and service providers to determine incentives, participation, pricing, or trustworthy behavior. The reviewed applications include dynamic, Bayesian, mixed-strategy, and market-oriented games.

Non-cooperative and Stackelberg games differ in timing: players act simultaneously in the former, whereas leaders move before followers in the latter.
Dynamic games: A two-level dynamic game models FL training-service markets through evolutionary MDG selection and differential-game pricing strategies.MOs select mobile device groups using prices and time-varying accuracy, while MDGs optimize prices in response to selections.
Bayesian games: A Bayesian game incentivizes prediction-service providers to participate and choose model quality, using accuracy-aware payments and deposits for unfulfilled promises.
Mixed-strategy games: A mixed-strategy game detects bad client updates by combining client choices between good or bad updates with server acceptance or rejection decisions.At equilibrium, simulations detected 100% of bad clients and improved test accuracy by 15.8% in flipping scenarios and 2.3% in noisy scenarios over prior methods.
Cross-silo markets: Cross-silo FL incentive mechanisms let heterogeneous organizations report training capacity and desired rewards, after which transfers and costs determine organizational payoffs.

C. Incentive Mechanisms Based on Other Game Methods

Other game methods address participation, clustering, federation formation, and privacy-aware cooperation among FL participants. The reviewed mechanisms include participation, hedonic, coalitional, contract, consensus, and reverse-game approaches.

Participation games: Participation games model each edge device’s decision to join an FEL round as a payoff trade-off between service income and local training and updating costs.Correlated equilibrium and decomposed global-profit subproblems are used to identify participation strategies; devices with larger data contributions are more likely to participate.
Hedonic games: Hedonic games model data-owner agents as selectively forming clusters, with cluster utilities combining raw utility and learning utility.
Contract and federation mechanisms: Contract theory motivates workers, while federations of model owners are formed selectively to maximize their individual profits in mobile crowdsensing networks.
Consensus and privacy: A proof-of-FL consensus mechanism combines cooperative global-model training with reverse-game data trading that rewards utility only when training avoids privacy leakage.
Section synthesis: The reviewed game-theoretic mechanisms seek equilibrium solutions that maximize utility while satisfying individual rationality, incentive compatibility, and budget balance.

V. APPLICATIONS OF AUCTION FOR INCENTIVE MECHANISM DESIGN IN FL

Auction mechanisms allocate FL participants and resources under strategic information and multiple-service settings. The reviewed approaches use sealed bids, double auctions, priority-based matching, cooperative allocation, and learning-enhanced auction design.

Auction foundations: Auctions support FL incentives by encouraging truthful reporting through incentive compatibility and ensuring non-negative participant utility through individual rationality.
Sealed-bid auctions: Sealed-bid auctions collect private bids, costs, and capacities from data owners, then repeatedly select qualifying winners until the FL task is completed.
Double auctions: FEST uses bidder selection, task allocation, and worker payment assignment to match buyers with high-quality sellers under resource, energy, workload, and execution constraints.Seller priority combines task bid, execution time, and seller preference; payments reward high-quality service and punish inadequate quality.
Multiple FL services: Multi-FL auction and allocation settings address coexisting services by optimizing intra-service bandwidth and then distributing bandwidth among service providers.
Learning-enhanced auctions: A deep learning-based auction uses historical data to address information asymmetry and lets workers earn higher revenue than under a conventional second-price auction.
Auction-coalition allocation: A joint auction-coalition framework allocates UAV coalitions to worker cells to mitigate communication-link failures and missing nodes in FL.

3) VCG Auction:

The survey reviews auction-based incentive mechanisms for FL, including VCG variants, reverse auctions, and related selection schemes that balance participant quality, cost, welfare, and fairness. These approaches differ in how they elicit bids, select clients, allocate payments, and address information asymmetry or data-quality constraints.

VCG Auction: Fair-VCG extends VCG by incentivizing data owners to contribute data and truthfully report costs while reducing unfairness without requiring the server to know cost types or data quality.It calculates a data acceptance vector and payment vector, with an adjustment payment obtained through neural-network-based optimization.
VCG Auction: The proposed FVCG mechanism addresses supply-side information asymmetry and fairness among data owners, while demand-side information asymmetry motivates additional game-theoretic mechanisms.The survey distinguishes supply-side uncertainty from demand-side uncertainty concerning users’ valuations of trained FL models.
Reverse Auctions: Reverse auctions let resource sellers bid their acceptable prices, helping model owners elicit training costs and reduce incentive expenses through winner selection and task assignment.The typical process includes bidding, winner selection, and task assignment.
Reverse Auctions: 400% larger social welfare than a fixed-price scheme was achieved by a reverse combinatorial auction that jointly optimized resource bids, local accuracy, energy cost, winner selection, and payments.The fixed-price mechanism depends heavily on resource prices, whereas the proposed method solves winner selection through social welfare maximization.
Reverse Auctions: Auction mechanisms also select participants using data quality or reputation, but EMD-based approaches require the global distribution of all data, which is impractical in FL.RRAFL instead uses reputation to select reliable mobile devices and update their reputation after training.
Reverse Auctions: Randomized auction schemes formulate winner selection as social-cost minimization and can guarantee an approximation factor relative to optimal minimum cost, but one such scheme omits bidder privacy protection.Users bid with uplink transmission power, CPU frequency, training cost, and related resources to maximize utility.

VI. APPLICATIONS OF CONTRACT AND MATCHING THEORY FOR INCENTIVE MECHANISM DESIGN IN FL

This section reviews contract- and matching-theoretic incentive mechanisms that model private information, participant selection, payments, and utility in federated learning. The surveyed approaches address heterogeneous costs, data distributions, network settings, and task preferences through contracts, matching, or both.

Contract theory: Contract mechanisms model the model owner as offering contracts that data owners select according to their private abilities and utility.The model owner designs contracts without knowing each data owner’s private type; each data owner selects the contract maximizing its utility.
Contract theory: Task-aware contracts represent FL tasks through rewards and update cycles to trade off service latency and age of information.The model owner sets contracts for different training tasks while workers choose an optimal contract.
Contract theory: In electric-vehicle networks, non-collaborative energy contracts improve charging-station utilities by 48% and social welfare by 36% over other economic models.Charging stations use FL-based demand predictions before reserving energy from the smart-grid provider.
Contract theory: Multi-dimensional contracts incorporate training cost, communication delay, and non-IID data when deriving model-owner-optimal contracts.Under non-IID data, the model owner may select multiple types, and weakly incomplete information generally increases cost relative to complete information.
Contract and matching theory: A UAV sensing mechanism combines multi-dimensional contract design with traversal-cost compensation and Gale-Shapley matching to assign low-cost UAVs to sensing regions.Simulation results demonstrate incentive compatibility and matching efficiency.

B. Incentive Mechanisms Based on Matching Theory

This section situates matching theory as a tool for worker selection in FL and summarizes broader incentive-mechanism findings and unresolved design challenges. The review emphasizes utility, revenue, latency, adaptability, and participation constraints.

Matching theory: Matching theory supports worker selection because its two-sided matching rule is suited to requesters of FL services.The passage identifies optimal two-side matching as the relevant property for worker selection.
Section summary: The reviewed contract and matching applications seek to maximize seller utility or revenue and buyer profit while minimizing FL training latency.The section’s related works are summarized in Table VI.
Section summary: Traditional contract designs rely mostly on optimization methods, while deep-reinforcement-learning-based designs are suggested for adapting to changing user types.The recommendation is presented as a future direction for contract design.
Section summary: Economic and game-theoretic models have been widely applied to incentive schemes across different FL scenarios, but incentive-mechanism design remains in its infancy.The survey identifies open issues and future research directions following this assessment.
Related challenge: Offline auction mechanisms may force bidders to wait until enough bids are available, including bidders who ultimately lose.This waiting behavior can discourage participation.

1) Online-Auction based Mechanism Design:

This section identifies unresolved issues in incentive-mechanism design, including adversarially robust contribution evaluation, privacy protection, multi-objective optimization, adaptive technologies, and heterogeneous rewards. The survey concludes by organizing economic and game-theoretic approaches and outlining future research directions.

Contribution evaluation: Shapley-value contribution evaluation commonly assumes an honest trusted server and does not account for adversarial participant behavior that can make evaluations unfair.The survey calls for comprehensive and transparent contribution-evaluation mechanisms.
Privacy protection: Existing incentive mechanisms may expose data owners’ private preferences during bidding, while losing bidders receive no compensation for that disclosure.The survey links this design gap to reduced participation enthusiasm and calls for joint incentive and privacy protection.
Multi-objective design: Many mechanisms optimize a single objective, although participant selection and contribution evaluation should be jointly considered in FL.The passage gives performance maximization and fairness as examples of separate objectives.
Future directions: Deep reinforcement learning has produced good results in incentive design, while graph neural networks, generative adversarial networks, and multi-agent reinforcement learning are proposed for new scenarios.The suggested scenarios include mobile edge computing and 5G/B5G.
Multiple incentive schemes: Current FL systems mainly use monetary incentives even though participants may prefer different reward types and individualized schemes.The survey highlights unresolved questions about assigning reward types and adapting schemes when new participants arrive.
Conclusion: The survey reviews FL fundamentals, economic and game models, incentive-mechanism applications, and open research directions.Its stated contribution is a comprehensive survey of economic and game-theoretic approaches to FL incentive design.